Lemma 2.1 (Lemma 20.3 in [1]}) 
Let \(E\)  be an inner product space,
\(V\)  a vector field,
and \(f:E\rightarrow V\)  a surjective linear map.
Then \(f\)  induces an inner product on \(V\)  such that the norm of \(v\in V\)  is
\(\Vert v\Vert _{V}=\min \lbrace \Vert u\Vert _E\mid f(u)=v\rbrace .\) 

